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Existence and Number of Global Solutions to Model Nonlinear Partial Differential Equations

Galstyan, Anahit

Abstract Details

2005, PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences.
In this dissertation we studied nonlinear partial differential equations in two different directions. We apply the bifurcation theory to investigate a number of positive solutions of the semilinear Dirichlet boundary value problem on a n-dimensional ball for the second order elliptic equation with periodic nonlinearity containing a positive parameter. Our approach appeals to the well known results of B. Gidas, W.-M. Ni, L. Nirenberg, the bifurcation theorems of M. G. Crandall and P. H. Rabinowitz, and the stationary phase method. Further, we investigate the issue of global existence of the solutions of the Cauchy problem for the semilinear Tricomi-type equations, appearing in the boundary value problems problems of gas dynamics. We study Cauchy problem trough integral equation and give some sufficient conditions for the existence of the global weak solutions. We prove necessity of these conditions. We obtain necessary condition for the existence of the self-similar solutions for the semilinear Tricomi-type equation. In our approach we employ the fundamental solution and the Lp-Lq estimates for the linear Tricomi-type equations.
Dr. Philip Korman (Advisor)
130 p.

Recommended Citations

Citations

  • Galstyan, A. (2005). Existence and Number of Global Solutions to Model Nonlinear Partial Differential Equations [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115841126

    APA Style (7th edition)

  • Galstyan, Anahit. Existence and Number of Global Solutions to Model Nonlinear Partial Differential Equations. 2005. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115841126.

    MLA Style (8th edition)

  • Galstyan, Anahit. "Existence and Number of Global Solutions to Model Nonlinear Partial Differential Equations." Doctoral dissertation, University of Cincinnati, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115841126

    Chicago Manual of Style (17th edition)